Set the Instant Pot to ‘Sauté’ mode and heat the olive oil.
Add the diced onion and sauté for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the chicken pieces to the pot and sauté for 3-4 minutes, stirring occasionally, until the chicken is lightly browned on all sides.
Add the rinsed rice, chicken broth, water, salt, black pepper, dried thyme, and paprika to the pot. Stir to combine.
Close and seal the Instant Pot lid. Set to ‘Manual’ or ‘Pressure Cook’ mode on high pressure for 8 minutes.
When the cooking cycle is complete, perform a quick release of the pressure.
Open the lid and immediately add the chopped broccoli florets on top of the rice and chicken mixture. Do not stir.
Close the lid again and let the residual heat steam the broccoli for 5 minutes with the Instant Pot off.
After 5 minutes, open the lid and stir in the shredded cheddar cheese, shredded mozzarella cheese, sour cream, and grated Parmesan cheese until everything is well combined and the cheese is melted.
Taste and adjust seasoning if needed.
Serve warm.